What set of coefficients balances the equation using standard form (lowest whole number ratios)? _CH4 + _O2 → _CO2 + _H2O
Understand the Problem
The question is asking for the correct set of coefficients that balance the provided chemical equation, specifically in its lowest whole number ratios.
Answer
The set of coefficients that balances the equation is $1, 2, 1, 2$.
Answer for screen readers
The balanced equation is: $$ 1\text{ CH}_4 + 2\text{ O}_2 \rightarrow 1\text{ CO}_2 + 2\text{ H}_2\text{O} $$ So the coefficients are 1, 2, 1, 2.
Steps to Solve
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Write the unbalanced equation
The given equation is: $$ \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} $$
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Count the number of atoms of each element
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Reactants:
- Carbon (C): 1 (from $\text{CH}_4$)
- Hydrogen (H): 4 (from $\text{CH}_4$)
- Oxygen (O): 2 (from $\text{O}_2$)
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Products:
- Carbon (C): 1 (from $\text{CO}_2$)
- Hydrogen (H): 2 (from $\text{H}_2\text{O}$)
- Oxygen (O): 3 (2 from $\text{CO}_2$ + 1 from $\text{H}_2\text{O}$)
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Balance the hydrogen atoms
To balance the hydrogen atoms, we place a coefficient of 2 in front of $\text{H}_2\text{O}$: $$ \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} $$
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Re-count the atoms after balancing hydrogen
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Reactants:
- C: 1
- H: 4
- O: 2
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Products:
- C: 1
- H: 4 (2 from 2 $\times \text{H}_2\text{O}$)
- O: 4 (2 from $\text{CO}_2$ + 2 from 2 $\times \text{H}_2\text{O}$)
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Balance the oxygen atoms
To balance the oxygen atoms, we place a coefficient of 2 in front of $\text{O}_2$: $$ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} $$
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Final count of atoms
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Reactants:
- C: 1
- H: 4
- O: 4 (2 from 2 $\times \text{O}_2$)
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Products:
- C: 1
- H: 4
- O: 4
The equation is now balanced.
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The balanced equation is: $$ 1\text{ CH}_4 + 2\text{ O}_2 \rightarrow 1\text{ CO}_2 + 2\text{ H}_2\text{O} $$ So the coefficients are 1, 2, 1, 2.
More Information
Balancing chemical equations is crucial for understanding chemical reactions and stoichiometry. The coefficients represent the number of molecules or moles involved in the reaction, and it ensures that the law of conservation of mass is upheld.
Tips
- Forgetting to balance one of the atoms (usually oxygen).
- Using fractions instead of whole numbers; always express coefficients as integers.
- Miscounting atoms while balancing.
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